H & K,
I am sure that the weight you listed is not the curb weight of that model truck, which is in the range of Curb weight: 4,517 to 5,670 lbs
...depending on cab style, etc. Maybe the 6300 pounds you quoted is a max weight with payload?
However, even at the lowest unloaded curb weight, this is a towed vehicle that is probably a bit too much for the RV to handle. A good rule of thumb for any towing application is to not exceed 75% or 80% of ratings to have a good margin of safety. That said, a towed car of about 4000 pounds seems like a good target for your motor home.
For my Tour Master diesel pusher, the tow rating is 10,000 pounds. The 2005 Acura MDX has a curb weight of 4,608 pounds so with personal belongings in the car it was under 5,000 pounds at all times...lots of margin there for my coach but still too much for your present rig.
Be safe and stay within ratings...and always use a good quality brake controller and auxiliary braking system and a properly rated tow bar.